The Moral Obligation to Break Laws: An Axiomatic Approach

1 Introduction 

Liberty is integral to a moral society. No society can claim to be moral and indulge in the infringement of basic human rights and essential freedoms.1 Though laws may at times be designed to accommodate, specify, and protect the freedoms of its subjects, it is not necessarily the case that such a trait can be extended to all laws, as there may exist laws that are amoral or immoral. Amoral laws, although irrelevant to the subject at hand, may relate to issues in particular sub-fields of tort law (e.g. traffic regulations) that do not involve moral judgment and exist to encourage and maintain order. For example, such laws may exist to produce economically efficient outcomes through the allocation of liabilities in the event of unintentional accidents. In contrast, immoral laws unnecessarily infringe upon individual freedoms and result in inefficient outcomes. The necessity or obligation of a legal intervention can be determined axiomatically by examining whether a society is more free as a result of the implementation of the law. Likewise, the obligation to undermine the legitimacy of law through extrajudicial means can be determined by examining whether society is less free as a result of the existence of such a law. 

2 The Concept of Liberty in Society

2.1 Individual Actions 

Every individual has a set of actions. An action is an exercise of one’s capacity. We may therefore denote the set or domain of actions of an individual, i, with the letter Ai. More specifically, Ai = {A0, A1, ..., Aj}. This means that the ith individual can exercise j + 1 distinct actions throughout the course of one’s lifetime, where j is an arbitrary natural number. A society can be represented by the set of each bundle of rights/freedoms every individual has; we may formally express a society, S, in the following manner: S = {A0, A1, ..., Ak}, where k, also an arbitrary natural number, stands for the number of people in the society. The liberty of each individual i can be expressed as a function that maps each Ai, where Ai = {A0, A1, ..., Aj}, to j + 1. In other words, one’s liberty is equivalent to the number of actions that one can perform. This is usually referred to as the cardinality of the set Ai, which is denoted by |Ai|. We may now proceed with the following definitions. 

Definition 1 (Individual’s Action Set): The set of actions Ai for an individual i is defined as Ai = {A0, A1, ..., Aj}, representing the actions available to the individual i. 

Definition 2 (Society): A society S is represented by the collection of individual action sets, defined as S = {A0, A1, ..., Ak}. 

Definition 3 (Liberty as Cardinality): The liberty of an individual i is expressed as the cardinality of their action set Ai, or |Ai|. 

Given two distinct individuals x and y with their respective sets of actions Ax and Ay, we define a function fy that models the impact of an action taken by individual x on the cardinality of the action set available to individual y. 

Definition 4 (Impact Function): The function, fy, maps an action from individual x’s action set and the current cardinality of y’s action set to a new cardinality of y’s action set and is defined as fy : Ax × N → N. 

Let |Ay|, |A′y| ∈ N, where each element stands for the liberty of individual y before and after individual x exercises an action, respectively. The function maps an action from x and the current cardinality of y’s action set to the new cardinality of y’s action set, |A′y|, after x’s action has been taken into account. If the selection of action An by individual x results in a reduction in the cardinality of y’s action set, we can express it in the following manner: 

|A′y| < |Ay| 

Definition 5 (Unjust or Morally Impermissible Action): If there exists an action, An, in Ax that gives rise to the inequality |A′y| < |Ay|, then An is unjust or morally impermissible, as it leads to a reduction in the number of actions available to individual y, thereby reducing y’s liberty. 

2.2 The Rule of Law 

In a state of anarchy, the absence of laws allows any action to be selected, often leading to a sub-optimal set of available actions for the community. This necessitates the creation of the rule of law. 

Definition 6 (Rule of Law and Remedial Action): Let Ax and Ay represent the action sets of individuals x and y, respectively. If an action Ak ∈ Ax satisfies the condition outlined in Definition 5, such that its execution results in the inequality |A′y| < |Ay|, thereby reducing the liberty of individual y, then the rule of law mandates a just remedy. This remedy is formalized by the removal of action Ak from Ax, denoted as Ax \{Ak}. This remedial action upholds the principles of justice by directly addressing and rectifying instances where individual liberties are compromised. 

3 Extrajudicial Justification 

3.1 Morally Impermissible Laws 

Laws are instituted to preserve the cardinality of all individuals’ actions by prohibiting actions that infringe upon the liberties of other individuals. Nevertheless, laws can sometimes be designed sub-optimally, reducing the overall cardinality of possible actions. 

Definition 7 (Unjust or Morally Impermissible Law): If the law enforces Ax \ {Ak} and the condition set in Definition 6, namely, |A′y| < |Ay|, is not met for any Ay ∈ S, then the law is unjust. This condition illustrates that the law’s enforcement diminishes x’s liberty unnecessarily without a corresponding justification through the preservation of y’s liberty. 

3.2 Existence of the Obligation to Break Unjust Laws under the Rule of Law 

Proof. Let there exist a law, Ax \ {Ak}, for any Ax ∈ S, such that it is unjust under Definition 7. Let the law be syntactically equivalent to the action Al of individual k + 1 (i.e. the government) and is an element of Ak+1. Since Ax \ {Ak} is unjust, Alis unjust. Therefore, under Definition 6, Ak+1 \ {Al}  would be necessary for the preservation of justice.

4 Conclusions 

• Laws that unnecessarily reduce the cardinality of the action set of an individual are not morally permissible. 

• It is morally permissible to break laws that are themselves not morally permissible, as they infringe upon individual liberties. 

By Daniel Lu